GP-equivalent posterior for a Quantum Kernel Ridge Regression fit

Given a fitted quantum_krr_fit() model, returns the predictive posterior at new inputs as an edaphos_posterior(). Using the well-known equivalence between Kernel Ridge Regression and Gaussian-process regression (Rasmussen & Williams 2006, §2.3), the predictive variance is derived analytically from the same gram matrix K + lambda I that produces the point prediction. Aleatoric noise is estimated from leave-one-out residuals.

Usage

quantum_krr_posterior(object, newdata, n_samples = 500L, units = NULL)

Arguments

object

An edaphos_quantum_krr.

newdata

A matrix (or data frame) with ncol(newdata) == object$n_qubits.

n_samples

Integer; the Gaussian posterior is analytic, so sampling is only needed for the edaphos_posterior machinery (CRPS estimation etc.). Defaults to 500L.

units

Optional free-text units tag.

Value

An edaphos_posterior with method = "analytic" and query_type = "sample". The epistemic/aleatoric decomposition is carried through post$epistemic_sd and post$aleatoric_sd.

References

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press, §2.3.